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Question Number 85542 by TawaTawa1 last updated on 22/Mar/20

Commented by TawaTawa1 last updated on 22/Mar/20

$$\mathrm{Evaluate}:\underset{x\to \frac{\mathrm{x}}{2}}{\lim }(\mathrm{x}-\frac{\pi }{2})\tan \mathrm{x}$$

Commented by mathmax by abdo last updated on 22/Mar/20

$$letf\left(x\right)=(x-\frac{\pi }{2})tanxchangementx-\frac{\pi }{2}=tgive$$$$f\left(x\right)=ttan(\frac{\pi }{2}+t)=t\frac{sin(\frac{\pi }{2}+t)}{cos(\frac{\pi }{2}+t)}=t\frac{cost}{-sint}=-\frac{t}{tant}$$$${lim}_{x\to \frac{\pi }{2}}f\left(x\right)={lim}_{t\to 0}-\frac{1}{\left(\frac{tant}{t}\right)}=-1$$

Commented by TawaTawa1 last updated on 22/Mar/20

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by turbo msup by abdo last updated on 23/Mar/20

$$youarewelcomemisstawa$$

Answered by jagoll last updated on 22/Mar/20

$$\underset{x\to \frac{\pi }{2}}{\lim }(\mathrm{x}-\frac{\pi }{2})\cot (\frac{\pi }{2}-\mathrm{x})$$$$\underset{\mathrm{t}\to 0}{\lim }\frac{-\mathrm{t}}{\tan \mathrm{t}}=-1$$

Commented by TawaTawa1 last updated on 22/Mar/20

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Commented by TawaTawa1 last updated on 22/Mar/20

$$\mathrm{Sir},\mathrm{help}\mathrm{me}\mathrm{solve}\mathrm{question}85546$$

Commented by jagoll last updated on 23/Mar/20

$$\mathrm{writting}\mathrm{is}\mathrm{too}\mathrm{small},\mathrm{i}\mathrm{did}\mathrm{not}$$$$\mathrm{clearly}\mathrm{read}\mathrm{it}$$

Commented by TawaTawa1 last updated on 23/Mar/20

$$\mathrm{Thank}\mathrm{you}\mathrm{sir},\mathrm{please}\mathrm{check},\mathrm{i}\mathrm{retype}.$$

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